Download Experimental Design and Data Analysis

Workshop overview
The workshop will comprise lectures and computer practical sessions over two weeks of
integrated presentations.
1. Non-parametric multivariate analyses of ecological data, using PRIMER v6 (first week)
Prof K Robert Clarke (PRIMER-E, Plymouth Marine Laboratory) & Ray Gorley (PRIMER-E)
Bob Clarke will lecture on simple, non-parametric approaches to analysing assemblage data, and
associated environmental information, using the PRIMER v6 statistics package for Windows
(Plymouth Routines In Multivariate Ecological Research, www.primer-e.com) The core features
in PRIMER cover a range of univariate, graphical and multivariate routines: hierarchical
clustering into sample (or species) groups (CLUSTER); ordination by non-metric multidimensional scaling (MDS) and principal components (PCA) to summarise patterns in species
composition and environmental variables; permutation-based hypothesis testing (ANOSIM), an
analogue of univariate ANOVA which tests for differences between groups of (multivariate)
samples from different times, locations, experimental treatments etc; identifying the species
primarily providing the discrimination between two observed sample clusters (SIMPER); the
linking of multivariate biotic patterns to suites of environmental variables (BEST/Bio-Env);
comparative (Mantel-type) tests on similarity matrices (RELATE); standard diversity indices;
dominance plots; species abundance distributions and curves; aggregation of arrays to allow data
analysis at higher taxonomic levels; and matching of sample patterns from different faunal arrays
(BEST/BvStep, a stepwise algorithm generalising Bio-Env which can be used, for example, to find
‘influential species’, and 2STAGE, a second-stage MDS in which relationships between a large
set of ordinations can be visualised). Another widely-used feature is the ability to calculate
biodiversity indices based on the taxonomic (or phylogenetic/functional etc) relatedness between
the species making up a species list or quantitative sample, indices which are robust to variations
in sampling effort. These routines (TAXDTEST) permit hypothesis tests for biodiversity change
and comparison over wide space and time scales.
Lectures will also cover: dispersion-weighted similarities, which downweight contributions
from abundant but highly variable species; new permutation tests for significance of: a)
dominance curves, b) optimal biota to environment relations found by BEST (adjusting for
selection bias) and c) groups found by a cluster analysis of a priori unstructured samples
(SIMPROF test); also generalisation of the similarity percentage breakdowns (SIMPER) to twoway layouts; non-parametric linkage trees (LINKTREE), which relax the implicit constraint in
BEST of additive environmental effects on community composition; relatedness-based similarity
measures included in the nearly 50 (dis)similarity /distance coefficients offered; treatment of
missing data by the EM algorithm, and many other practical features.
PRIMER v6 will be used throughout this 5-day initial component of the workshop, in the lab
sessions which are interspersed with the lectures, using the PRIMER software already installed
on the lab machines. This will allow the participants to try out the methods on literature data sets,
and they are also encouraged to bring along some of their own data to try out, under the guidance
of Bob Clarke and Ray Gorley (PRIMER-E). Ray will be assisting in the lab sessions in both
weeks. The final two afternoon sessions of the first week have been set aside for one-to-one
discussions with Bob and Ray on individuals' design and analysis questions.
2. Multivariate analysis of complex experimental designs, using PERMANOVA+ (second
week)
Prof Marti J Anderson (Massey University, New Zealand) & Ray Gorley (PRIMER-E)
The second half of the course will concentrate on the analysis of multivariate data in response to
more complex models, experimental designs or sampling designs. All of the methods covered
here share certain important qualities with the routines offered in the core PRIMER routines:
they can be based on a dissimilarity (or similarity) measure of choice (so are quite flexible) and
results of tests of hypotheses are obtained using permutation techniques (making them quite
robust approaches which lack the usual assumptions of traditional statistics). The software used
will be the PERMANOVA+ add-on package to the PRIMER v6 software, developed by Marti
Anderson and Ray Gorley. This package is sold as a separate add-on to PRIMER v6, and has
been coded by Ray Gorley in the same Microsoft .Net2 environment as PRIMER, hence
integrating seamlessly with it. Emphasis in this second week will be placed on the logical design
and analysis of experiments and observational studies, as well as the use and interpretation of the
software, given this logic.
The topics to be covered, identifiable as individual routines in the new software, include:
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PERMANOVA, for the analysis of univariate or multivariate data in response to factors,
groups or treatments in an experimental design;
PERMDISP, to measure and test homogeneity of multivariate dispersions among a priori
groups;
PCO, to provide an unconstrained ordination of multivariate data on the basis of a chosen
resemblance measure;
DISTLM, for the analysis of univariate or multivariate data in response to explanatory or
predictor variables that are continuous (such as environmental variables), as in a
regression or multiple regression;
dbRDA, for the ordination and visualisation of fitted models (such as from DISTLM);
CAP, for constrained ordination and to use multivariate data to discriminate among a
priori groups or to predict values along gradients of continuous or ordered variables.
Special topics covered will also include (among others) tests and interpretations of interaction
terms for multivariate data, nested designs, fixed versus random factors, constructing specific
contrasts among treatments or groups of treatments, designs with covariates, unbalanced designs
(including choosing appropriate types of sums of squares), methods of permutation, using
asymptotic Monte Carlo P values when there aren’t enough possible permutations for a test,
asymmetrical designs, pooling or excluding terms, designs that lack replication, repeated
measures, tests of dispersion, beta diversity, the difference between constrained and
unconstrained ordination for visualising multivariate data, drawing and interpreting biplots,
model selection, and designs for detecting environmental impacts.
Lectures will again be interspersed with computer practical sessions on literature data sets, using
the lab machines on which the PERMANOVA+ software is already installed (participants are
free to bring their own laptops in addition, if they hold valid software licences for these; check
with Cathy or Marg at [email protected] for licence status). The whole of the last day will
offer an opportunity for the participants to explore the analysis of their own data sets using the
methods and software lessons from both weeks of the workshop.
Biographies of lecturers and demonstrators
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Prof K Robert Clarke (PRIMER-E) holds a first class Hons degree in Mathematics (University
of Leicester 1969), an M.Sc and Ph. D. in Statistics (University of Newcastle, 1970, 1976) and
lectured for several years in the University of Glasgow Statistics Department before moving to
Plymouth (1979), where over the next 20+ years he had prominent roles both as a statistical
research scientist (ultimately IMP grade 6, professorial equivalent) and a member of the
executive management of the Plymouth Marine Laboratory (PML). In 2000 and 2001 he held a
Visiting Professorship in the University of Sydney. Prof Clarke is now a Director of a spin-out
company (PRIMER-E Ltd), undertaking statistical consultancy and software development, and
has been awarded Honorary Fellowships at the PML and the Marine Biological Association of
the UK and an adjunct professorship at Murdoch University, WA. He has published about 90
refereed papers in SCI-listed journals, a few of the more highly cited of which are listed below,
and from 2004 has been included in the 'ISIHighlyCited' listing of the world's top-cited authors
in Plant and Animal Science. He has given many invited lectures to international conferences in
statistics (International Biometric Society, International Environmetrics Society, Sydney
International Statistics Congress, Royal Statistical Society) and environmental science (SETAC,
Washington; MacMillan Biodiversity Lecture, Vancouver etc), and led many academic
workshops on statistical analysis of environmental data, e.g. under the auspices of IOC, FAO and
UNEP, and numerous commercial training workshops all over the globe. Prof Clarke is
responsible for the development of the PRIMER package (www.primer-e.com) for statistical
analysis of community data, now used by ecologists and environmental scientists worldwide.
Some well-cited and more recent publications [SCI citations to May 2010 in brackets]:
Field, J.G., Clarke, K.R., Warwick, R.M. 1982. A practical strategy for analysing multispecies
distribution patterns. Mar Ecol Prog Ser 8, 37-52 [948]
Clarke, K.R., Green, R.H. 1988. Statistical design and analysis for a 'biological effects' study.
Marine Ecology Progress Series 46: 213-226 [754]
Clarke, K.R. 1993. Non-parametric multivariate analyses of changes in community structure.
Australian Journal of Ecology 18: 117-143 [2,540]
Clarke, K.R., Ainsworth, M. 1993. A method of linking multivariate community structure to
environmental variables. Marine Ecology Progress Series 92: 205-219 [582]
Clarke, K.R., Warwick R.M. 1994 and 2001. Change in Marine Communities:An Approach to
Statistical Analysis and Interpretation, 1st edition: Plymouth Marine Laboratory, Plymouth,
UK, 144pp. 2nd edition: PRIMER-E, Plymouth, UK, 172pp [3,402]
Clarke, K.R., Gorley, R.N. 2001 (and 2006). PRIMER v5 (and v6): User manual/tutorial.
PRIMER-E, Plymouth, UK, 91pp (and 192pp) [1,515]
Clarke, K.R., Warwick, R.M. 1998. Quantifying structural redundancy in ecological
communities. Oecologia 113: 278-289 [75]
Clarke, K.R., Warwick, R.M. 1998. A taxonomic distinctness index and its statistical properties.
Journal of Applied Ecology, 35: 523-531 [220]
Clarke, K.R. 1999. Non-metric multivariate analysis in community-level ecotoxicology.
Environmental Toxicology and Chemistry 18: 118-127 [52]
Clarke, K.R., Warwick R.M. 1999. The taxonomic distinctness measure of biodiversity:
weighting of step lengths between hierarchical levels. Marine Ecology Progress Series 184:
21-29 [101]
Clarke, K.R., Warwick R.M. 2001. A further biodiversity index applicable to species lists:
variation in taxonomic distinctness. Marine Ecology Progress Series, 216: 265-278 [150]
Clarke, K.R., Somerfield, P.J., Chapman, M.G. 2006. On resemblance measures for ecological
studies, including taxonomic dissimilarities and a zero-adjusted Bray-Curtis coefficient for
denuded assemblages. Journal of Experimental Marine Biology and Ecology, 330: 55-80 [76]
Clarke, K.R., Chapman, M.G., Somerfield, P.J., Needham, H.R. 2006. Dispersion-based
weighting of species counts in assemblage analyses. Marine Ecology Progress Series, 320: 1127 [18]
Clarke, K.R., Somerfield, P.J., Airoldi, L., Warwick, R.M. 2006. Exploring interactions by
second-stage community analyses. Journal of Experimental Marine Biology and Ecology, 338:
179-192 [6]
Clarke, K.R., Somerfield, P.J., Gorley, R.N. 2008. Exploratory null hypothesis testing for
community data: similarity profiles and biota-environment linkage. Journal of Experimental
Marine Biology and Ecology, 366: 56-69 [17]
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Mr Ray N Gorley (PRIMER-E) is responsible for producing all the Windows code for the
current PRIMER and PERMANOVA+ software packages. He obtained a 1st class degree in
Natural Sciences from Cambridge University UK (1975), specialising in Theoretical Physics and
Applied Maths. He started a PhD in Particle Physics, but, after a couple of years left to work in
industry, in the future systems department of an electronics company manufacturing radar
systems. He then joined a group at University College London, managing and writing the
software for an image processing system for processing meteorological images. In the early
1990's he joined Plymouth Marine Laboratory, working on the ECoS software package, for
simulating hydrodynamic and bio-geochemical processes in estuarine systems. His move to work
with Bob Clarke at PML came at the end of the millenium, helping to develop the Windows code
for what became PRIMER 5. This led to formation of the PRIMER-E Ltd spin out company
with Bob Clarke, late in 2000, in which Ray is a co-director and responsible for all software
development.
Selected Publications
Clarke, K.R., Gorley, R.N. 2001. PRIMER v5: User manual/tutorial. PRIMER-E, Plymouth, UK,
91pp
Clarke, K.R., Gorley R.N. 2006. PRIMER v6: User Manual/Tutorial. PRIMER-E, Plymouth,
UK, 192pp
Anderson, M.J., Gorley, R.N., Clarke, K.R. 2008. PERMANOVA+ for PRIMER: Guide to
Software and Statistical Methods. PRIMER-E, Plymouth, UK, 214pp
______________________________________________________________________________
Prof Marti J Anderson is a full Professor in the Institute of Information and Mathematical
Sciences of Massey University, New Zealand, where she holds the Chair of Statistics. She has
undergraduate qualification in Biology (BA, Occidental College, Los Angeles, 1991) and
graduate qualifications in Zoology (Grad.Dip.Sci. 1992), Marine Ecology (Ph.D. 1997) and
Mathematical Statistics (MA 1998), all from the University of Sydney. As an inter-disciplinary
ecological statistician, her work centres on the use and development of novel statistical methods
(particularly multivariate methods) for ecological applications (especially in marine systems). An
important aspect of this work is the development of computer programs for the implementation
of new statistical methods. Her special areas of interest and expertise include experimental
design and permutation tests for complex designs, on which she has published extensively, and is
widely cited. She is actively involved in research and consultancies for environmental impact
assessment and monitoring, as well as teaching and lecturing worldwide - since 1997 she has
been invited to present many intensive courses on multivariate analysis in ecology, globally.
Selected Publications
Tolimieri, N., Anderson, M.J. 2010. Taxonomic distinctness of demersal fishes of the California
current: moving beyond simple measures of diversity for marine ecosystem-based
management. PLoS ONE 5(5), e10653: 1-14.
Gotelli, N.J., Anderson, M.J., and others. 2009. Patterns and causes of species richness: a general
simulation model for macroecology. Ecology Letters 12: 873-886.
Anderson, M.J. 2008. Animal-sediment relationships revisited: characterising species’ distributions along an environmental gradient using canonical analysis and quantile regression
splines. Journal of Experimental Marine Biology and Ecology 366: 16-27.
Anderson, M.J., Ellingsen, K.E. and McArdle, B.H. 2006. Multivariate dispersion as a measure
of beta diversity. Ecology Letters 9: 683-693.
Anderson, M.J. 2006. Distance-based tests for homogeneity of multivariate dispersions.
Biometrics 62: 245-253.
Anderson, M.J. and Thompson, A.A. 2004. Multivariate control charts for ecological and
environmental monitoring. Ecological Applications 14: 1921-1935.
Millar, R.B. and Anderson, M.J. 2004. Remedies for pseudoreplication. Fisheries Research 70:
397-407.
Anderson, M.J. and Millar, R.B. 2004. Spatial variation and effects of habitat on temperate reef
fish assemblages in northeastern New Zealand. Journal of Experimental Marine Biology and
Ecology 305: 191-221.
McArdle, B.H. and Anderson, M.J. 2004. Variance heterogeneity, transformations and models of
species abundance: a cautionary tale. Canadian Journal of Fisheries and Aquatic Sciences 61:
1294-1302.
Anderson, M. J. and Robinson, J. 2003. Generalised discriminant analysis based on distances.
Australian & New Zealand Journal of Statistics 45(3): 301-318.
Anderson, M. J. and Willis, T.J. 2003. Canonical analysis of principal coordinates: a useful
method of constrained ordination for ecology. Ecology 84: 511-525.
Anderson, M. J. and ter Braak, C.J.F. 2003. Permutation tests for multi-factorial analysis of
variance. Journal of Statistical Computation and Simulation 73: 85-113.
Anderson, M. J. 2001. Permutation tests for univariate or multivariate analysis of variance and
regression. Canadian Journal of Fisheries and Aquatic Sciences 58: 626-639.
Anderson, M. J. 2001. A new method for non-parametric multivariate analysis of variance.
Austral Ecology 26: 32-46.
Anderson, M. J. and Robinson, J. 2001. Permutation tests for linear models. Australian and New
Zealand Journal of Statistics 43: 75-88.
McArdle, B. H. and Anderson, M. J. 2001. Fitting multivariate models to community data: a
comment on distance-based redundancy analysis. Ecology 82(1): 290-297.
Anderson, M. J. and Clements, A. 2000. Resolving environmental disputes: a statistical method
for choosing among competing cluster models. Ecological Applications 10: 1341-1355.
Anderson, M. J. and Legendre, P. 1999. An empirical comparison of permutation methods for
tests of partial regression coefficients in a linear model. Journal of Statistical Computation and
Simulation 62: 271-303.
Legendre, P. and Anderson, M. J. 1999. Distance-based redundancy analysis: testing multispecies responses in multi-factorial ecological experiments. Ecological Monographs 69: 1-24.